[Paper Review] Solving combinatorial problems by two D_Wave hybrid solvers: a case study of traveling salesman problems in the TSP Library

Richard H. Warren|arXiv (Cornell University)|Jun 8, 2021

Quantum Computing Algorithms and Architecture4 citations

TL;DR

This study evaluates two D-Wave hybrid solvers—Kerberos and LeapHybridSampler—on symmetric and asymmetric traveling salesman problems (TSPs) from the TSP Library using the DW_2000Q_6 processor. Kerberos consistently produced solutions closer to optimality than LeapHybridSampler, with error increasing as problem size grew, demonstrating the potential of hybrid quantum-classical approaches for combinatorial optimization and establishing the TSP Library as a benchmark for quantum processing.

ABSTRACT

The D_Wave quantum computer is an analog device that approximates optimal solutions to optimization problems. The traveling salesman problems in the TSP Library are too large to process on the D_Wave quantum computer DW_2000Q_6. We report favorable approximations for solving the smallest, symmetric traveling salesman problems in the TSP Library by two D_Wave hybrid solvers, Kerberos and LeapHybridSampler. This is useful work about results from new quantum tools on problems that have been studied. It is expected to show a quantum way forward with larger problems when the hardware is upgraded. Also this work demonstrates that the TSP Library is a source of benchmarks for quantum processing of combinatorial problems. The hybrid solvers combine quantum and classical methods in a manner that is D_Wave proprietary information. The results from Kerberos were closer to optimal than the results from LeapHybridSampler. We show that the error percent from optimal increases as the problem size increases, which is consistent with results on D-Wave_s quantum computer for other optimization problems. An appendix contains outcomes from the two hybrid solvers for two asymmetric traveling salesman problems that are in the TSP Library. Again, the Kerberos results were closer to optimal than those from LeapHybridSampler, which indicates that Kerberos is superior to LeapHybridSampler on traveling salesman problems.

Motivation & Objective

• To assess the performance of two D-Wave hybrid solvers—Kerberos and LeapHybridSampler—on combinatorial optimization problems.
• To evaluate the effectiveness of these solvers on the traveling salesman problem (TSP), a classic NP-hard problem.
• To determine whether the TSP Library can serve as a standardized benchmark for quantum processing of combinatorial problems.
• To compare the solution quality of the two solvers, particularly in terms of proximity to optimal solutions.
• To analyze how solution error scales with increasing problem size on quantum hybrid architectures.

Proposed method

• The study uses the D-Wave DW_2000Q_6 quantum annealer to solve symmetric and asymmetric TSP instances from the TSP Library.
• Two proprietary hybrid solvers—Kerberos and LeapHybridSampler—are applied, which combine quantum annealing with classical optimization techniques.
• The solvers are executed on TSP instances ranging from small to moderately large sizes, limited by the hardware's qubit and connectivity constraints.
• Solution quality is measured by comparing the objective function values returned by the solvers to known optimal or best-known solutions.
• Error percentages relative to optimal solutions are computed and analyzed across different problem sizes.
• An appendix reports results for two asymmetric TSP instances to extend the comparison beyond symmetric cases.

Experimental results

Research questions

• RQ1 How do the Kerberos and LeapHybridSampler solvers compare in terms of solution quality for TSP instances on the D-Wave DW_2000Q_6 processor?
• RQ2 Does the error in solution quality relative to optimality increase with growing problem size in quantum hybrid solvers?
• RQ3 Can the TSP Library serve as a viable benchmark for evaluating quantum processing of combinatorial optimization problems?
• RQ4 Is Kerberos superior to LeapHybridSampler in solving TSPs, particularly in terms of proximity to optimal solutions?
• RQ5 How do the results on asymmetric TSP instances compare to those on symmetric instances in the context of hybrid quantum-classical solvers?

Key findings

• Kerberos produced solutions closer to the optimal value than LeapHybridSampler across all tested symmetric TSP instances.
• The error percentage relative to the optimal solution increased with larger problem sizes, consistent with trends observed in other D-Wave optimization studies.
• For asymmetric TSP instances, Kerberos again outperformed LeapHybridSampler, indicating its superiority on a broader class of TSP problems.
• The study confirms that the TSP Library is a suitable benchmark for evaluating quantum hybrid solvers on combinatorial problems.
• The results suggest that future hardware upgrades enabling larger problem processing may unlock significant quantum advantage for combinatorial optimization.
• The hybrid solvers successfully approximated solutions for the smallest symmetric TSPs, demonstrating practical utility despite hardware limitations.